How to quickly separate and/or delete extra faces created by extruding?
By now you are working with "edge" selection mode (2nd button on the header).

Just switch to "faces" mode (the third), select the face you want to delete, press X and choose the preferred option.

Try also the first button (vertex mode).

The fourth on the right lets you also select  vertex, edges or faces hidden by some other geometry.



Another useful function is select some faces, hit P> Selection, then exit edit mode (&#8633; Tab). The selected faces will be no longer be a part of your original object: they are a brand new object.

Additionally if you hit Y instead of P the selection will be separated from the original mesh while remaining part of the same object.